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Question: How to find the integral

Question:How to find the integral

Markiyan Hirnyk 7759 Maple
closed-form improper-integral
February 22 2013
1

int(mul(sin(x/2^k)*2^k/x, k = 0 .. 123), x = 0 .. infinity) in closed form  with Maple?
I conjecture that the answer is Pi/2 and 123 can be replaced by any natural (i.e. ::posint) number.
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